Calculate the Reynolds numbers at the root chord location for the following aircraft. Assume that the density and dynamic viscosity of air at sea level are 0.002378 slug/ft’ and 3.737 x 107 slug/(ft•s): (a) A DC-3 with a wing root chord length 15.25 ft flying at 250 ft/s at sea level. (b) An F-22 with a wing root chord length 21.5 ft flying at 920 ft/s at sea level.

Please write down a related Average Nusselt number equation for each case. (Do not calculate) Laminar flow SCHEMATIC: Air 4∞ = 2 m/s Top = 25°C p = 1 atm w= 0.2 m L=25 AL 0.25 m T = 500 °C ASSUMPTIONS: (1) Top surface is smooth, (2) Bottom surface is adiabatic, (3) Critical Reynolds number is 5 × 105, (4) Negligible radiation.

(1) Experiments show that in a slightly Viscorur flund at on a молод high speeds the drag force fo exerted on body depends on several parametes. An engineer assumes that the drag force fo is a functon of the budy width normal to the upstream Velocity, I upstream Velouty, ✓, the upstream flud veElucay P viscosity, M, speed of sound, I and the airfoils surface roughnars. " use the Buckingham ♬ Theorem to determine the functional dependence of to on non-dimensional flow similarity parameters (2:) Lot the transition to turbulence occur when I = 1.01m, V= 1·01m/s and M₁P = 1:01·10⁰5 m² s. Calculate the transchen Reynolds number, Retrains.

2. The table below shows experimental data for the shape and pressure distribution on the upper and lower surface of an airfoil at zero angle of attack. X 0 0.25 0.5 0.75 1 Yu 0 0.0952 0.0922 0.0588 0 Fx = dYu dx 5 Y₁ 0 -0.0254 -0.0144 -0.0052 0 PL Pd) d: dx Y = Yu (x) Calculate the drag and lift force on the airfoil by numerically evaluating the integrals = S₁² ( P₂₁ = ['(P₁ - F (P₁ - Pu)dx 0 y = Y₂ (x) Pu 1.000 -1.640 -0.786 -0.212 0 Fy x Pi 1.000 0.589 0.426 0.322 0 Use finite difference approximations of the derivatives and the composite Simpson's rule to evaluate the integrals. Hint: Use central differences to estimate the derivatives wherever possible since they are more accurate than forward or backward differences.